Significance and probability Type I and II errors Practical Psychology 1 Week 10

2 Descriptive Statistics: a review  Describe numerical data  Communicate numerical findings in standardized (means, sd, N in the form of a table) & pictorial ways (bar chart)  Techniques for describing data: Figures (bar chart, pie chart, S&L plot, etc.) Measures of central tendency and dispersion (Mean, median, SD, range, etc.) RF, percentiles Distributions (Z-scores and SND curve  Next week)

3 E.g. Descriptive statistics table and figure

4 Inferential Statistics  Inferential statistics is based upon probability  Used to make inferences about whether the characteristics of a sample is a good representation of characteristics of the population.  Allow inferences to be made from the numerical findings.  Permit different kinds of conclusions to be reached (e.g. significant difference in driving ability between males and females)

5 What is probability?  Probability (p) describes random or chance events; refers to how likely a particular outcome is.  Event must be random, so outcome be determined by luck.  E.g. coin: p (getting Heads) = 1 in 2 or 0.5 or 50%  Probability can be expressed as a ratio, fraction, or percentage.  Probability of events occurring is measured on a scale from 0 (not possible)________________ to 1 (must happen).

6 Hypotheses… review  Usually stated in terms of the dependent (DV) and independent variables (IV).  Null Hypothesis  Experimental Hypothesis one-tailed (directional) two-tailed (non-directional)  It is on the basis of inferential testing that a hypothesis can be accepted or rejected.

7 Null hypothesis Ho  a null hypothesis is a hypothesis set up to be falsified in order to support an alternative hypothesis (  the experimental).alternative hypothesis  the null hypothesis is presumed true until statistical evidence in the form of a hypothesis test indicates otherwise.evidence  a null hypothesis is often the reverse of what the experimenter actually believes; it is put forward to allow the data to contradict it.

8  Social scientists reject the null hypothesis H 0 (that differences occur at a chance level only), when the probability of this being true drops below 0.05 (5%)... ...this is often called alpha (α), the “5% significance level”. Significance level α (alpha)

9 SPSS output

10 Significance level 5% 5% (0.05)  Conventional significance level.  if the p-value is close to 5% it may well be decided that the research is worth pursuing.  If a result is significant (p < 0.05 “less than 0.05”) the null hypothesis is rejected.  If a result is not significant (p ≥ 0.05 “greater than or equal to 0.05”) the null hypothesis is retained/ not rejected.  By 'result is significant' we mean 'the difference (or relationship) is unlikely to have occurred by chance at the set level'

11 Significance levels 1% (0.01)  Stricter, preferred for greater confidence than the conventional one  If we are about to challenge a well-established theory or research finding by publishing results which contradict it, the convention is to achieve 1% significance before publication.  When the researcher only has a one-off chance to demonstrate an effect (replication may be impossible in many field studies or “natural experiments”).

12  Significant difference at 5% (p<0.05) “the difference is significant” “the correlation is significant”  Significant at 1% (p<0.01) “the difference is HIGHLY significant” “the correlation is HIGHLY significant”

13 Significance level 10% (0.1)  Significance level generally considered too high for rejection of the null hypothesis, but which might merit further investigation.  a researcher cannot be confident of results, or infer an actual effect, if the level achieved is only 10%.

14 Type I and Type II errors  If the null hypothesis is true, but has been rejected because p<0.05, it is said that Τype I error has occurred.  A Τype II error occurs when the null hypothesis is retained, because p>0.05. Yet, there is a real underlying effect.

15 Type I and Type II errors  Type I error: Mistake made in rejecting the null hypothesis when it is true  Type II error: Mistake made in retaining the null hypothesis when it is false.

16 Type I and Type II errors Decision Null hypothesis H 0 is actually: AcceptedRejected True Type I error FalseType II error

Stay tuned for… Independent samples T-test